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7/27/2019 Anlisis de Espectro de poder En Bsqueda De Periodicidades En Datos de Serie de tiempo Irradiance Solares De E

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JOURNAL OF

Engineering Science and

Journal of Engineering Science and Technology Review 4 (1) (2011) 96-100 Technology Review

Research Article www.jestr.org

Power Spectrum Analysis In Search For Periodicities In Solar Irradiance Time

Series Data From Erbs

K. M. Hossain1,

*, D. N. Ghosh2, K. Ghosh

3and A. K. Bhattacharya

4

1Dpt of Electronics and Instrumentation Engineering, Dr. B.C. Roy Engineering College, Jemua Road, Fuljhore, Durgapur-713 206, India,

2Dpt of Mathematics, Dr. B.C. Roy Engineering College, Jemua Road, Fuljhore, Durgapur-713 206

3Dpt of Mathematics, University Institute of Technology, University of Burdwan, Golapbag (North), Burdwan-713 104, India,

4Dpt of Electronics & Communication, National Institute of Technology, Mahatma Gandhi Avenue, Durgapur-713209, India,

Received 10 June 2010; Revised 14 December 2010; Accepted 25 February 2011

Abstract

In the present paper we have analyzed the solar irradiance data from the Earth Radiation Budget Satellite (ERBS) duringthe time period from October 15, 1984 to October 15, 2003 to detect the corresponding periods, if any with relevant

scores (confidence). Power spectrum of the denoised signal has been obtained using FFT in order to search for itsperiodicities. Present calculation reveals strong periods around 9.08-9.35, 13.53-14.03, 27.50-28.17, 30.26, 35.99-36.37,51.14-51.52, 68.27-68.60, 101.15, 124.85, 150.63-153.98, 659.90, 729.37, 1259.82, 3464.50 and 4619.33 days. We alsogot some weak periods around 46.19, 72.55, 82.49, 137.21-139.98, 395.94, 407.59 and 1979.71 days.

Keywords: FFT, Power Spectrum, periodicities, scores, Solar Irradiance data

1. Introduction

Total Solar Irradiance (TSI) is defined as the

electromagnetic radiant energy emitted by the sun over allwavelengths that falls each second on 1 square meteroutside the earth's atmosphere. Solar irradiance refers to

electromagnetic radiation in the spectral range of

approximately 19ft (0.33m), where the shortestwavelengths are in the ultraviolet region of the spectrum,the intermediate wavelengths in the visible region, and thelonger wavelengths are in the near infrared. Total Solar

Irradiance indicates the solar flux integrated over all

wavelengths to include the contributions from ultraviolet,visible and infrared radiation.

The solar irradiance is been monitored with absolute

radiometers since November 1978, on board six spacecraft(Nimbus-7, SMM, UARS, ERBS, EURECA, and SOHO),outside the terrestrial atmosphere. Before measuring it from

space, this quantity was thought to be constant, because the

precision of the ground-based instruments at that time was

not high enough to detect small variation. It consequentlyearned the name of solar constant, which had a value ofonly 1,353 W/m

2. But from the data sent by the mentioned

spacecraft it has been revealed that the solar irradiance varies

about a small fraction of 0.1% over solar cycle being higher

during maximum solar activity conditions. [1]A major part of the Solar Irradiance variation is due to

the combined effect of the sunspots blocking and the

* E-mail address: [email protected]

ISSN: 1791-2377 2011 Kavala Institute of Technology. All rights reserved.

intensification due to bright faculae and plages, with a slightdominance of the bright features effect during the 11-yearsolar cycle maximum. Solar Irradiance variation within solar

cycle is thought to be due to the changing emission of bright

magnetic elements, including faculae and the magneticnetwork. [2]
http://www.jestr.org/http://www.jestr.org/mailto:[email protected]:[email protected]:[email protected]:[email protected]://www.jestr.org/


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The Solar Irradiance variation is very important for theunderstanding of solar internal structure and the solar

terrestrial relationships. The radiative outputs of the sun

establish the earths radiation environment and influenceits temperature and atmosphere. It has been indicated thatsmall persistent variation in energy flux may play an

important role in climate changes. [2]

It has been recognized that the variation of the solarirradiance data obtained by the Earth Radiation BudgetSatellite (ERBS) during the time period from October 15,

1984 to October 15, 2003 [3] has anti-persistent nature andthus it may have multi-periodicity [4]. In this paper we willtry to identify the possible periods of this solar irradiancedata and calculate their scores which are analogous to

statistical confidence levels. The prerequisite for this is tosmoothening and filtering the data to remove thecircumstantial errors (which may creep in due to change inenvironment, or systematic error which is due to factorsinherent in the manufacture of the measuring instrument

arising out of tolerances in the components of the

instruments) and the noises (contributed by the receiverthermal noise, losses in waveguides and waveguidecomponents, sky noise, interference entering the earth stationreceiving antenna, interference entering the satellite


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A2u

tnStep 1: :Discrete Derivative

Ste 4:Local Inte ralu

. . .t-t

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K. M . Hossain , D. N. Ghosh, K. Ghosh and A. K. Bhattacharya/Journal of Engineeri ng Science and Technology Review 4 (1) (2011) 96-100

receiving antenna, thermal noise generated in the satelliteand inter-modulation noise throughout the system). Here it

has been assumed that the power of the aggregate noise to be

almost constant for all the frequencies (i.e. white

noise).Smoothening and filtration has been done by FiniteVariance Scaling Method (FVSM) and Discrete WaveletTransform based filtering respectively. [5]

The data, after filtration, are up sampled by padding

zeroes at the missing data which is then operated by FastFourier Transform to get the coefficients in the frequency

domain. The coefficients are squared to get the power at

different frequencies nay at different periods. The peaks ofthis curve are then detected by the derivative and integralmethod algorithms. The scores of the peaks are finally

checked.

2. Theory

2.1 Power Spectrum Analysis In Search Of Periodicities

Of Solar Irradiance Variation

We carry out the power spectrum analysis of the denoisedsignal using Fast Fourier transform (FFT). The FFT of the

time series signal x[n] is given by X (fn) where X (fk) are the

coefficients of the frequency spectrum of x[n]. X (fk ) isrelated to x[n] by the equation

(1)

where, k=0,1,2, ............N-1 and T is the sampling interval.

In our case x[n] is the time series data of the denoised

solar irradiance with zero padding at the missing data. X (fn )

when plotted against the frequencies gives the frequencyspectrum of the data.

The square of the absolute magnitudes of the coefficientsgives the power of the signal at the different frequencies.

The plot of the power as a function of frequencies gives the

power spectrum of the signal. The power spectrum has someconfident peaks. The frequencies corresponding to thesepeaks can be taken as the strong frequencies within the time

series signal. The inverse of the frequencies gives the periods

within the signal. Plotting the power as the function of the

periods gives the periodogram.

2.2 Peak Detection Algorithm For The Search Of

Prominent PeaksFour different algorithms [5] have been used to detect thepeaks of the periodogram.The algorithms are derivative

based and integral based. If tnbe the discrete time then x[n]is represented by x(tn). x(tn) represents the power at theinstant tn.

2.2.1 Derivative MethodsThree algorithms are being used which are based onderivatives methods.The methods are as follows:xt ( ) ( ) (n)-x t

n+1 n=A1xt

Step 2:Score

Step3: Data Set Stratification

The vector of S0 is sorted as per their magnitude.

2.2.1.2 Method 2

n

Step1: Discrete Derivative

Step 2:Score

Step 3: Data Set Stratification


2.2.1.3 Method 3

Step 1: :Discrete Derivative

Step 2:Scoren

xtn 1 n 1 x tt t

n1 n

xtA1

tn

Step3: : Data Set Stratification


2.2.2 Method 4 (Integral Method)

Step1:Integral

x t


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=argmax(Ax(tn))Step 2:Discrete Derivative

t n

Step 3: Maximum Localisation


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Step 5: Score

. A vector of S0 is obtained.

Step 6: Data Set Stratification


3. Results

Fig.1 represents the original signal of the daily SolarIrradiance from October, 1984 to October, 2003 obtained byERBS.

1368

1367

1366

1365

1364

1363

1362

1361

1360

Fig. 1.

Daily TSI data from October 1984 to October 2003Year----->

Fg1:DailyTSIdatafromOtober1984toOctober2003

Fig.2 shows the signal after simple exponential smoothingand denoising. Discrete Wavelet Transform (DWT) with softthresholding has been used for denoising. [4]

Fig. 2. Signal obtained after DWT Threshold Denoising

Fig.3 shows the frequency spectrum of the data obtained after

FFT.

Fig. 3. Frequency Spectrum after FFT on the denoised signal

The power spectrum obtained is shown in fig.4. From thefig.4 we see the power spectrum has some confident peaks.

Fig.4. Power Spectrum on the denoised signal

The periodogram is shown in fig.5. In this plot the powers at

higher frequencies are neglected as they may be noisepowers.

Fig. 5. Power VS Periods curves of the denoised signal

The peaks has been detected by using the derivative andintegral algoritms as discussed earlier. The scores of the

periods corresponding to these peaks are being calculated.

The periods along with their scores are shown in table 1 foreach methods of peak detection algorithms.

Table 1. Scores obtained for each periods using peakdetection algorithm

Method 1 Method 2 Method 3 Method 4

Periods Scores Periods Scores Periods Scores Periods Scores

9.344572 1 .25E*11 9.350877 3. 35E*10 9.338275 1.88E*11 9.075311 2.08E-01

14.01213 6.18E*1 1 14.02632 2.15E*11 13.99798 9.38E*11 13.5332 3.60E-01

28.10953 1 .15E*11 28.16667 3. 04E*10 28.05263 1.73E*11 27.49603 1.13E-01

30.25764 7.71E*0 9 30.25764 4.14E*09 36.3727 1.16E*10 35.99481 1.08E-02

68.26601 1 .07E*10 68.60396 3. 89E*09 51.13653 1.83E*10 51.51673 1.14E-02

124.8468 9 .18E*09 153.9778 3. 88E*09 150.6304 1.73E*10 101.1533 4.15E-03

729.3684 1 .37E*10 729.3684 1. 06E*10 659.9048 2.45E*10 659.9048 3.98E-03

4619.333 1.09E*10 1259.818 3.13E*09 3464.5 1.62E*10 4619.333 2.63E-03

Following figures (Figures 6-9) depict the profiles obtainedby Methods1-4 respectively.


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Fig.6. Scores of periods using Method 1



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From the fig 6,7,8 and 9 it is evident that the periods in the

range of 9.08 to 9.35 days are very strong. Other strong

peaks are around 13.53-14.03, 27.50-28.17, 30.26, 35.99-

36.37, 51.14-51.52, 68.27-68.60, 101.15, 124.85, 150.63-

153.98, 659.90, 729.37, 1259.82, 3464.50 and 4619.33

days. Some weak periods have also being noticed around

46.19, 72.55, 82.49, 137.21-139.98, 395.94, 407.59 and

1979.71 days.

4. Discussion

The variation of solar irradiance data may provide an

indication for a secular change that might be related to subtlechange in the solar radius [6, 7]. Short term changes of solar

irradiance data during solar activity cycles are expected to be

due to the luminosity changes connected with the

temperature fluctuation of the solar surface and may also be

due to the redistribution of the solar radiation by sunspot andactive region population. We compare our results with the

corresponding published periodicities of other solar activities

in table 2.

Table 2. Comparative study of the obtained periods with other

solar activity periods

Serial No. Solar Activities Periods

Obtainedsimilarperiods in thepresent work

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

23

24

25

26

Solar X-ray Flares andCoronal Mass ejections

during Solar Cycle 23 [8]

Solar Filament Activity[9]

Solar electron flareoccurrence [10]

Solar Flare Rate [11]

Solar Proton events [12]

Solar Magnetic Cloud[13]

Mean solar magneticfield [14]

Solar Chromosphereduring the last three solarcycles [15]

The near-Earth solar

wind during the last three

solar cycles [15]

Interplanetary magnetic

field during the last three

solar cycles [15]Geomagnetic activity

during the last three solarcycles [15]

Solar Neutrino Flux [16]

Solar Neutrino Flux [17]

Total area of coronal

holes enclosed within alatitude band of 1050 S[18]

Polar Coronal holes area

[19]Solar rotation at itsequator [20]

Solar rotation at its pole[21]

Solar total and UV

irradiances, 10.7 cm radio

flux, Ca-K plages index,

and sunspot blockingfunction [22]

Sunspot numbers &

Sunspot areas [23]

Solar rotation duringcycle22 [24]

Solar rotation duringcycle23 [24]

Solar flare occurrenceCycle 19 [26]Solar flare occurrence

Cycle 20 [26]

Solar flare occurrenceCycle 21 [26]

Solar flare occurrenceCycle 23 [26]

14 days

367, 795, 1141 and 1557 days

152 days for cycle 21, 330 and604 days for cycle 22 and 152

days and 176 days for thecurrent cycle 23

51, 78, 102, 128 and 154 days

154 days

7 and 32 days

14 days

13.5 days

13.5 days

13.5 days

13.5 days

For 5 day long samples 7.5,

699.9, 1012.5 and 1282.5 daysFor 10 day long sample 15, 30,845, 1575 days For45 day long samples 495 and855 days

13.75 days(strongest period)

38.82 days(secondstrongest

period)

592 days

66 days

25 days

36 days

13.5, 51, 150-157 and 240-330days

Between 23.1 and 36.4 days

2741 days

2445 days

51 days

84 and 129 days

153 day

33.5 and 129 days

13.53-14.03 days

395.94, 729.37and 1259.82days

150.63-153.98and 395.94days

51.14-51.52,

82.49, 101.15,124.85 and150.63-153.98 days

150.63-

153.98 days

9.08 -9.35 and30.26 days

13.53-14.03 days

13.53-14.03 days

13.53-

14.03 days

13.53-14.03 days

13.53-

14.03 days

9.08 -9.35,13.53-14.03,

30.26, 729.37

and 1259.82days

13.53-14.03

and 35.99-36.37 days

659.90 days

68.27-68.60

27.50-28.17

35.99-

36.37 days

13.53-14.03,

51.14-51.52,150.63-153.98

and 395.94days

27.50-28.17,

30.26 and35.99-36.37

days 27.50-28.17,

30.26 and35.99-36.37

days 27.50-28.17,

30.26, 35.99-

36.37 and46.19 days

51.14-51.52

82.49 and

124.85 days150.63-153.98 days35.99-36.37

and 124.85days


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It is pretty much understandable from the above tableand from our results that the periodicities of the Total SolarIrradiance variation have significant resemblance with the

periodicities for other different solar activities. So it may beinterpreted that as a whole solar irradiance has closeassociation with other solar activities.

References

1. Oncica, M.D. Popescu, M. Mierla, G. Maris, Do Flares Count forthe Variation of Total Solar Irradiance?, Proc. ESA SP-506, the10th European Solar Physics Meeting: "Solar Variability: From

Core to Outer Frontiers", Prague, 193-196, 2002.

2. P. Raychaudhuri, Total solar irradiance variability and the solar

activity cycle, Astrophysics, 601, 10,(2006).3. http://www.ngdc.noaa.gov/stp/solar/irradiance/erbs.html.

4. K. M. Hossain, D. N. Ghosh and K. Ghosh., Scaling Analysis by

FVSM and DWT denoising of the measured values of solarirradiance, International Journal of Information and ComputingScience, India, 12(2) ,1(2009).

5. Azzini R. DellAnna, F. Ciocchetta F. Demichelis, A.Sboner, E.Blanzieri A. Malossini, Simple Methods of Peak detection in

time series Microarray data,

http://www.camda.duke.edu/camda04/papers/days/thursday/azzini/paper.pdf.

6. P. Raychaudhuri, The Sun, C12/C13 abundance ratio andneutrino emission, Astrophysics and Space Science, 13, 231-233(1971).

7. P. Raychaudhuri, Origin of Stellar Magnetic Fields,

Astrophysics and Space Science, 18, 425-436 (1972).

8. A A Hady, The Periodicities of Solar X -ray Flares and Coronal

Mass ejections during Solar Cycle 2, Proceedings of theInternational Astronomical Union, 107-108 (2004).

9. W.B. Songa, J.X Wanga, A Study of the Periodicities of SolarFilament Activity, Chinese Astronomy and Astrophysics, 31 (3),270-276, (2007).

10. P. Chowdhury, P. C. Ray, Evaluation of the intermediate -termperiodicities in solar and cosmic ray activities during cycle 2,Monthly Notices of the Royal Astronomical Society, 373 (4), 191-201, (2007).

11. Y.Q. Lou, Rossby-Type Wave - Induced Periodicities in Flare

Activities and Sunspot Areas or Groups during Solar Maxima,The Astrophysical Journal, 540, 1102-1108, (2000).

12. S. Gabriel, R. Evans and J. Feynman, Periodicities in theOccurrence Rate of Solar Proton Events, Solar Physics, 128 (2),

415- 422(1990).

13. P. Raychaudhuri, Variations of Coronal Mass Ejections andSolar Proton Events (E >10 MEV ), 29th International CosmicRay Conference , Pune, 153-156, (2005).

14. T.K. Das and T.K. Nag, A 14-day periodicity in the mean solar

magnetic field, Solar Physics, 187 (1), 177-188 (1999).

15. K. Mursula and B. Zieger, The 13.5-day periodicity in the Sun,

solar wind and geomagnetic activity: The last three solar cycles,Journal of Geophysical Research, 101, 27077-27090, 1966.

16. K. Ghosh and P. Raychaudhuri, http://arxiv.org/ftp/astro-ph/papers/0606/0606082.pdf.

17. P. A. Sturrock, Time-Series Analysis of Super-KamiokandeMeasurements of the Solar Neutrino Flux, The Astrophysical

Journal, 594, 1102-1107, (2003).

18. P. S. Mclntosh, R. J. Thompson & E. C. Willock, A 600-day

periodicity in solar coronal holes, Nature 360, 322-324, (1992).

19. T. K. Das, T. N. Chatterji, T. Roy and A. K. Sen, Sixty six day

periodicity of polar coronal holes,Astrophysics and SpaceScience, 213 (2), 327-330, (1994).

20. K. Saxena, Principles of Modern Physics. Oxford: Alpha Science,

2005.21. "Sun." The Columbia Encyclopedia, Sixth Edition. 2008.

22. J. Pap, W. K. Tobiska and S. D. Bouwer, Solar Physics,Periodicities in solar irradiance and activity indices, SolarPhysics, 129 (1), 165-168, (1990).

23. H. Kili, Short-Term Periodicities in Sunspot Activity and Flare

Index Data during Solar Cycle 23, Solar Physics, 255 (1),155-162, (2009).P.Chowdhury , M. Khan and P. C. Ray,Intermediate-term periodicities in sunspot areas during solar

cycles 22 and 23, Monthly Notices of the Royal AstronomicalSociety, 39 (3), 1159-1180, ( 2008).

24. J. L. Ballester, R. Oliver and M. Carbonell, the near 160 dayperiodicity in the photospheric magnetic flux, The Astrophysical

Journal, 566, 505-511, (2002).25. T. Bai, periodicities in solar flare occurrence: analysis of cycles1923, The Astrophysical Journal, 591, 406-415(2003).
http://www.ngdc.noaa.gov/stp/solar/irradiance/erbs.html.http://www.ngdc.noaa.gov/stp/solar/irradiance/erbs.html.http://www.camda.duke.edu/camda04/papers/days/thursday/azzinhttp://www.camda.duke.edu/camda04/papers/days/thursday/azzinhttp://arxiv.org/ftp/astro-http://arxiv.org/ftp/astro-http://arxiv.org/ftp/astro-http://www.camda.duke.edu/camda04/papers/days/thursday/azzinhttp://www.ngdc.noaa.gov/stp/solar/irradiance/erbs.html.

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